11-08-24 AP Calculus AB VL Ch 3 Review

Front

What is the relationship between the derivatives of inverse functions?

Back

If g(x) = f^{-1}(x), then g'(x) = 1 / f'(g(x)).

Tags

CCSS.HSF-BF.B.4A

Front

What is the Chain Rule in calculus?

Back

The Chain Rule states that if you have a composite function f(g(x)), then the derivative is f'(g(x)) * g'(x).

Front

How do you find dy/dx using implicit differentiation for the equation f(x)g(y) = C?

Back

Differentiate both sides with respect to x, applying the product rule and chain rule as necessary, and solve for dy/dx.

Front

What is the derivative of ln(x)?

Back

The derivative of ln(x) is 1/x.

Front

How do you differentiate a function of the form f(g(x))?

Back

Use the Chain Rule: f'(g(x)) * g'(x).

Front

What is the second derivative of a function?

Back

The second derivative is the derivative of the first derivative, denoted as f''(x).

Front

What is the fourth derivative of y = 2 ln(x)?

Back

The fourth derivative is -12/x^4.

Front

What does it mean for a function to be differentiable?

Back

A function is differentiable at a point if it has a defined derivative at that point, meaning it is smooth and continuous.

Front

What is the product rule in calculus?

Back

The product rule states that if you have two functions u(x) and v(x), then the derivative of their product is u'v + uv'.

Front

How do you find the derivative of a logarithmic function?

Back

Use the derivative rule for logarithms: d/dx[ln(u)] = (1/u) * (du/dx).